Vibrational Playback Experiments: Challenges and Solutions

Abstract

Playbacks are one of the most useful experimental tools in animal communication research. Playbacks of substrate vibrations present special challenges, but conducting high-fidelity vibrational playbacks is not difficult and depends less on the specific equipment used than on avoiding some common pitfalls. We review the major issues, describing both the problems and a range of solutions. Our focus is on playback through living plants, but most of the issues apply to playback through other substrates as well. The major challenge for playback through any substrate is that the vibrational signal is almost always changed by the playback equipment and the substrate, so that the signal received by the focal animal is different from the one intended by the experimenter. The general solution to this problem is to measure the changes imposed by the playback system and to pre-filter the playback signal to compensate for them. A second challenge is to ensure that the focal animal receives a signal at the appropriate amplitude. Achieving the proper amplitude is a straightforward process. However, amplitude is substrate dependent (e.g., on a plant, amplitude is inversely proportional to stem diameter), and the experimenter should choose a realistic amplitude for the substrate. Other issues include choices of playback device, natural versus artificial substrates, single versus multiple substrate exemplars, and playback in laboratory versus field. Our goal in this chapter is to give experimenters, especially those just starting out, the knowledge and confidence needed to conduct high-quality vibrational playbacks.

Appendix

The following MATLAB programs use the Signal Processing Toolbox and the Control System Toolbox and have been confirmed to work in MATLAB 6.5 (R13) through to MATLAB 8.1 (R2013a).

1.1 Digital Equalization Filter

This program obtains the system equalization filter from stored measurements. A typical system would include the digital-to-analog converter, amplifier and vibration exciter, vibration medium, measurement transducer, anti-aliasing filter, and analog-to-digital converter. Prior to running this code, a continuous random signal (stored in WAVE file ‘Playback1.wav’) is played through the system, and the response is measured and saved (WAVE file ‘Recording1.wav’).

The power spectral density functions are estimated and used to obtain the magnitude of the input-to-output transfer function. The useful data range is taken between the specified lower and upper frequencies in hertz (variables ‘f_lo’ and ‘f_hi’), and the digital filter coefficients are estimated and saved (MATLAB data file ‘FilterCoefs.mat’). For evaluation purposes, the equalization filter is applied to the original playback signal and stored (WAVE file ‘Playback2.wav’). Arbitrary signals of different duration can be filtered this way using the identified filter coefficients, as long as the sample rates are the same.

MATLAB script for acquiring and implementing digital equalization filter:

• close all, clear all

• [out,fs,NBITS]=wavread(‘Playback1.wav’); %WAVE file with original playback

• [in,fs,NBITS]=wavread(‘Recording1.wav’); %WAVE file with recorded signal dt=1/fs;

• t_out = [0:dt:(length(out)-1)*dt];

• t_in = [0:dt:(length(in)-1)*dt];

• fftLength=4096;

• [PSDout,Freq]=pwelch(out,ones(fftLength,1),[],fftLength,fs);

• [PSDin,Freq]=pwelch(in,ones(fftLength,1),[],fftLength,fs);

• Hcmp=sqrt(PSDout./PSDin); %Amplitude compensation filter

• f_lo=40; f_hi=10000; %lower and upper cutoff frequencies in Hz.

• lo=round(f_lo/(fs/fftLength))+1;

• hi=round(f_hi/(fs/fftLength))+1;

• Hcmp(1:lo)=0; Hcmp(hi:length(Hcmp))=0;

• wn=Freq/max(Freq);

• B=fir2(fftLength,wn,Hcmp); %this calculates the digital filter coefficients

• A=1;

• save FilterCoefs.mat B A

• outcmp=filter(B,A,out); %this applies the digital filter to the signal

• outcmp=outcmp*.9/max(abs(outcmp));

• wavwrite(outcmp,fs,16,’Playback2.wav’);

1.2 Differentiation and Integration of Playback Signal

This MATLAB script numerically differentiates and integrates the time signal stored in a WAVE file (‘ArbPlayback.wav’). Differentiation of the signal can be approximated using the finite difference method (with ‘diff.m’), while integration of the signal can be approximated using trapezoidal integration (with ‘cumtrapz.m’). These methods work well if the time step is sufficiently small and if there is no noise in the signal.

When the signal has additional noise, the higher-frequency noise is increased by the differentiation process, while the lower-frequency noise is increased by integration. This noise can be reduced by using a first-order band-pass filter to perform the differentiation or integration. The band-pass center frequency is set to a high frequency for differentiation (variable ‘f_hi’), so the frequencies below the center frequency approximate a differentiation filter, while frequencies above are attenuated. For integration, the center frequency is set to a low frequency (variable ‘f_lo’), so frequencies below the center frequency are attenuated, while frequencies above approximate an integration filter. The appropriate center frequency also depends on the frequency content of the signal.

MATLAB script for differentiation and integration of playback signal:

• wavfile=‘ArbPlayback.wav’; %WAVE file name with playback signal

• [out,fs,NBITS]=wavread(wavfile);

• dt=1/fs;

• nt=length(out);

• t_out =[0:dt:(nt-1)*dt];

• %numerical differentiation by finite difference:

• outdiff=diff(out)/dt;

• outdiff(nt)=outdiff(nt-1);

• %numerical integration by trapezoidal rule:

• outint=cumtrapz(t_out,out);

• % Differentiation filter: Band pass filter with high corner frequency

• f_hi=10000; %upper cutoff frequency in Hz.

• SYSc=tf((2*pi*f_hi)^2*[1 0],conv([1 f_hi*2*pi],[1 f_hi*2*pi])); SYSd=c2d(SYSc,1/fs,’foh’);

• [Bcmp,Acmp]=tfdata(SYSd);

• outfiltdiff=filter(Bcmp{1},Acmp{1},out);

• % Integration filter: Band pass filter with low corner frequency

• f_lo=10; %lower cutoff frequency in Hz.

• SYSc=tf([1 0],conv([1 f_lo*2*pi],[1 f_lo*2*pi]));

• SYSd=c2d(SYSc,1/fs,’foh’);

• [Bcmp,Acmp]=tfdata(SYSd);

• outfiltint=filter(Bcmp{1},Acmp{1},out);